Standard mathematical notation to indicate whether the endpoint is or is not included.

  { x : a < x && x < b }  <=>  (a,b)
  { x : a <=x && x < b }  <=>  [a,b)
  { x : a < x && x <=b }  <=>  (a,b]
  { x : a <=x && x <=b }  <=>  [a,b]

In the example above the questioner is asking about getting a number in the range 1 to X inclusive. That would be [1,X]. Random number generators can return numbers in the range 0 to 1, including 0, not including 1. You can write that as [0,1).

If you want an integer n in [1,X] and you get reals r [0,1), you can create a function:

    f : [0,1) -> [1,X], f(r) = 1+floor(X*r)

Always check the endpoints, and the expected frequencies.